Critics of President Obama are lining up to bash his response to Russia's invasion of Ukraine's Crimean Peninsula, with many calling for the president to take a tougher stance against the machinations of President Vladimir Putin.

Sen. John McCain (R-Ariz.), for example, has called on Obama to revive the Bush-era missile defense plan, which would have placed U.S. missiles in the Czech Republic and Poland. He also believes that speeding up Georgia's membership into NATO would send a strong message to Putin, surrounding Russia with a ring of NATO-allied states.

For its part, the Obama administration is mulling visa-denials for regime figures, kicking Russia out of the Group of Eight, and freezing Russian assets to make Putin and the Russian oligarchy feel the consequences of his violation of Ukrainian sovereignty.

But let’s not kid ourselves — a tougher approach won't solve anything. Putin went to war in Georgia in 2008 when George W. Bush was president, even though you probably couldn't have found a more ardent advocate of American military interventions abroad. Bush was also in the midst of implementing that missile defense system in Eastern Europe, while welcoming former Eastern Bloc countries into NATO. The effect on Putin? Nada.

Meanwhile, Obama's approach has its flaws, too. Given Russia’s geographic size, natural resources, industrial capacity, and links with other countries outside Washington’s sphere of influence (especially China), the proposed actions may have little real effect on Putin’s power base. Perhaps most importantly, Russia supplies Western Europe with natural gas, one of the reasons Germany seems unwilling to take stronger action against Putin's regime.

But it charges high prices, and the dependence on Russian gas also makes Europe vulnerable from a national security standpoint. In the past, Russia has cut off natural gas supplies to Europe — often in the depths of winter — to achieve its objectives. For these reasons, Europe is often seeking alternative supplies.

This opens the door to America — which also has massive supplies of natural gas. If America really wants to undermine Putin’s regime and his ability to project power into Europe — or at the very least deter Putin from any further incursions into former Soviet republics — then developing the infrastructure to sell natural gas cheaply to Europe is the way to do it.

Naturally, this is a long-term strategy. But it is far more effective than counter-punching and military build-up. By shifting to an economic strategy, the U.S. can dodge the fight Putin is looking for, and hit him where it really hurts.